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How do I solve for x and y?

How do I solve for x and y?-example-1
User Jeff Brady
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Answer:

x = 80

y = 160

Explanation:

The sum of all arc measures that make up a circle is 360°. Therefore:


\implies 200^(\circ) + y^(\circ) = 360^(\circ)


\implies 200^(\circ) + y^(\circ) - 200^(\circ) = 360^(\circ) - 200^(\circ)


\implies y^(\circ) = 160^(\circ)


\implies y=160

Tangent and Intersected Chord Theorem

If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one-half the measure of its intercepted arc.

Therefore, according to the Tangent and Intersected Chord Theorem, the measure of angle x is equal to half of the measure of arc y:


\implies x^(\circ)=(1)/(2) y^(\circ)


\implies x^(\circ)=(1)/(2) \cdot 160^(\circ)


\implies x^(\circ)=80^(\circ)


\implies x=80


\hrulefill

Circle Theorem vocabulary

  • Chord: A straight line joining two points on the circle.
  • Tangent: A straight line that touches a circle at only one point.
  • Arc: the curve between two points on the circumference of a circle
  • Intercepted arc: The curve between the points where two chords or line segments intercept the circumference of a circle.
How do I solve for x and y?-example-1
User Msrdjan
by
8.8k points

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